Cryptic crossword No 3,749

Across

1. Beginnings of resource estimate (3)
2. Amended concerning nonsense we spread around (7)
3. Ardent followers pay for amateur mind reader show initially (15)
4. He sang beautifully - a part Vito messed up (9)
5. Negotiation has pub profiting (10)
6. Boredom has bunnies removing clothes and dancing (5)
7. Short piece of dreadful recital (7)
8. Challenging one hears pretty well, it's said (7)
9. Pile up in Eastern city where nothing is new (5)
10. Trick prisoner (3)
11. Appalling rain; vehicle crashes - leading to death of self (7)
12. Health centre near deprived area providing a bit of food? (9)
13. Bit of a wind-up sent me running around headland (10)

Down

1. Battersea and Bankside, for instance are places under control (5,8)
2. C.E.O. Fred ordered coffee - perhaps as deterrent (5,2,6)
3. A little mongrel I effectively help (6)
4. Take decisive action and try not to get stung (5,3,6)
5. Outlaw singer's top cover (7)
6. Massage crania with gel, perhaps (6)
7. Very bland however it appears (3,3)
8. Angry aliens rave about shelter - they refuse to go! (4,10)
9. Sea life leaving trap could be O.K. (6)
10. Fake vitamins lead to protectionist policy (8)
11. Greatest generosity: Tesla given for son (7)
12. French one caught you in Marseille house, naked and greasy (8)